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Uniqueness of the maximum likelihood estimates of the parameters of an ARMA model

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2 Author(s)
Astrom, K.J. ; Lund Institute of Technology, Lund, Sweeden ; Soderstrom, T.

Estimation of the parameters in a mixed autoregressive moving average process leads to a nonlinear optimization problem. The negative logarithm of the likelihood function, suitably normalized, converges to a deterministic function as the sample length increases. The local and global extrema of this function are investigated. Conditions for the existence of a unique global and local minimum are given.

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Automatic Control, IEEE Transactions on  (Volume:19 ,  Issue: 6 )